Metallic MOS: Difference between revisions

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Another way to think about the period is the interval from <math>\frac 01</math> to <math>\frac 11</math> (these are not frequency ratios, but just another way of writing 0 and 1, the motivation for which will become clear soon). We can find slightly more complex metallic generators by choosing an interval other than the entire period to split into two segments related by <math>φ</math>. For example, we could pick <math>\frac 13</math> to <math>\frac 12</math>, giving us approximately <math>0.419821</math>:

[[File:Noble generator.png|618x618px]]

[[File:Noble generator fixed.png|618x618px]]

Disclaimer: while these two segments are indeed related by , it is not simply by their lengths, as it may appear in the diagram. For now, let it suffice to say that extensions of the golden mean such as this are known as [http://mathworld.wolfram.com/NobleNumber.html noble numbers].<math>φ</math>As for why the order of the segments is flipped here — well, that too will be explained later.

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 Another way to think about the period is the interval from <span><math>\frac 01</math></span> to <span><math>\frac 11</math></span> (these are not frequency ratios, but just another way of writing 0 and 1, the motivation for which will become clear soon). We can find slightly more complex metallic generators by choosing an interval other than the entire period to split into two segments related by <span><math>φ</math></span>. For example, we could pick <span><math>\frac 13</math></span> to <span><math>\frac 12</math></span>, giving us approximately <span><math>0.419821</math></span>:
-[[File:Noble generator.png|618x618px]]
+[[File:Noble generator fixed.png|618x618px]]
 Disclaimer: while these two segments are indeed related by , it is not simply by their lengths, as it may appear in the diagram. For now, let it suffice to say that extensions of the golden mean such as this are known as [http://mathworld.wolfram.com/NobleNumber.html noble numbers].<span><math>φ</math></span>As for why the order of the segments is flipped here — well, that too will be explained later.